different ways to make 8

Free Worksheets, Lessons, Quizzes

• Kindergarten
• Kindergarten Numeracy Skills
• Kindergarten Addition

Number Bonds of 8

Number Bonds of 8: How many more to make 8? Find the missing number that makes 8 with the given number.

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Online addition practice for learning number pairs or number bonds with addition flashcards. Online addition flashcards to learn number bonds or number pairs of Making 8 is an ideal kindergarten online addition practice worksheet to develop basic addition skills. Try this online addition practice to learn all the addition facts to make 8. These online addition flashcards teach basic addition facts which are all the combinations of 1-digit numbers that add up to 8. Help your kid try this online kindergarten addition practice to develop his or her knowledge in making number pairs or number bonds to make 8 by using addition facts. Enjoy this fun kindergarten online addition practice activity for finding missing numbers to make number pairs.

Number Bonds of 8 Addition Flashcards Worksheet: Hit the ‘Check Your Answers’ button at the end to correct each answer of your making 8 online addition practice. These online addition flashcards worksheets are for learning basic kindergarten addition facts with number bonds or number pairs and to improve speed and accuracy of basic kindergarten addition skills. Enjoy learning the ways of making number pairs to make numbers with our online addition flashcards worksheets!

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Making 8, 9 and 10 Lesson: Game Worksheet

Students practice computation strategies and identify number patterns and relationships to make eight, nine, and ten in a variety of ways.

Matching Number Pairs for Eight Matching Number Pairs for Nine Matching Number Pairs for Ten Sample Lesson Making 7, 8, 9, 10 Worksheet Sums up to Five Sums up to Ten Worksheets

Operations & Algebraic Thinking

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from..

Combinatorics

Magic filters, display font, add/roll dice, random numbers, number converters, number formats, number lists.

Number Bonds for 8

Related Topics: Lesson Plans and Worksheets for Kindergarten Lesson Plans and Worksheets for all Grades More Lessons for Kindergarten Common Core For Kindergarten

Eureka Math/EngageNY Kindergarten, module 4, lesson 9 Common Core Worksheets.

New York State Common Core Math Kindergarten, module 4, lesson 9 Worksheets for Kindergarten

Worksheets, solutions, and videos to help Kindergarten students learn how to model decompositions of 8 using a story situation, arrays, and number bonds.

Topic B: Decompositions of 6, 7, and 8 into Number Pairs

Learning Goal:

• I can model decomposing 8 using a story, arrays, and number bonds.
• I know the number bonds for 8.

Number Bond for 8 Worksheet

Lesson 9 Concept Development and Problem Set

Take one of your 5-sticks. Add 1 more cube. How many cubes are in your stick now? (6.) Add 1 more cube. How many are in your stick now? (7.) Add another cube. Now how many cubes are in your stick? (8.) Take your 8-stick apart. Work with your partner to make two rows of cubes out of your stick. Make sure you have the same number of cubes in each row. How many cubes are in each row? (4.) Yes, you took your 8 and made 2 rows of 4! Now take your cubes and make a tiny row of 2. Make another tiny row of 2 underneath. Keep going until all of your cubes are used up. How many cubes are in each row? (2) How many tiny rows do you have? (4). You made your 8 into 4 rows of 2! You made your 8 into 2 columns. Talk to your partner about the ways you made your 8 look. Fill in the number bond to match the picture. Draw some more dots to make 8 dots in all and finish the number bond. Draw 8 dots, some blue the rest red. Fill in the number bond. Draw a line to make 2 groups of dots. Fill in the number bond.

• What are some of the ways you found to make a 7? Let’s put them in a list!
• How did you find all of those different ways? How did you know that you had found a way to make 7?
• In the Problem Set, what does the number 5 represent? How about the number 2? And the number 7?
• Did the story you and your partner told match the amount you put in each circle of the number bond?
• Why do we have to color all the cubes in the stick in the Problem Set?

Lesson 9 Homework Complete the number bond to match the dot picture. Draw a line to make 2 groups of dots. Fill in the number bond. Draw a number bond for 4. Fill in the number bond. Draw a number bond for 5. Fill in the number bond. Draw a number bond for 6. Fill in the number bond. Draw a number bond for 7. Fill in the number bond.

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Combinations and Permutations Calculator

Find out how many different ways to choose items. For an in-depth explanation of the formulas please visit Combinations and Permutations .

For an in-depth explanation please visit Combinations and Permutations .

Power Users!

The "has" rule which says that certain items must be included (for the entry to be included).

Example: has 2,a,b,c means that an entry must have at least two of the letters a, b and c.

The "no" rule which means that some items from the list must not occur together.

Example: no 2,a,b,c means that an entry must not have two or more of the letters a, b and c.

The "pattern" rule is used to impose some kind of pattern to each entry.

Example: pattern c,* means that the letter c must be first (anything else can follow)

Put the rule on its own line:

Example: the "has" rule

a,b,c,d,e,f,g has 2,a,b

Combinations of a,b,c,d,e,f,g that have at least 2 of a,b or c

Rules In Detail

The "has" rule.

The word "has" followed by a space and a number. Then a comma and a list of items separated by commas.

The number says how many (minimum) from the list are needed for that result to be allowed.

Example has 1,a,b,c

Will allow if there is an a , or b , or c , or a and b , or a and c , or b and c , or all three a,b and c .

In other words, it insists there be an a or b or c in the result.

So {a,e,f} is accepted, but {d,e,f} is rejected.

Example has 2,a,b,c

Will allow if there is an a and b , or a and c , or b and c , or all three a,b and c .

In other words, it insists there be at least 2 of a or b or c in the result.

So {a,b,f} is accepted, but {a,e,f} is rejected.

The "no" Rule

The word "no" followed by a space and a number. Then a comma and a list of items separated by commas.

The number says how many (minimum) from the list are needed to be a rejection.

Example: n=5, r=3, Order=no, Replace=no

Which normally produces:

{a,b,c} {a,b,d} {a,b,e} {a,c,d} {a,c,e} {a,d,e} {b,c,d} {b,c,e} {b,d,e} {c,d,e}

But when we add a "no" rule like this:

a,b,c,d,e,f,g no 2,a,b

{a,c,d} {a,c,e} {a,d,e} {b,c,d} {b,c,e} {b,d,e} {c,d,e}

The entries {a,b,c}, {a,b,d} and {a,b,e} are missing because the rule says we can't have 2 from the list a,b (having an a or b is fine, but not together)

Example: no 2,a,b,c

Allows only these:

{a,d,e} {b,d,e} {c,d,e}

It has rejected any with a and b , or a and c , or b and c , or even all three a,b and c .

So {a,d,e) is allowed (only one out of a,b and c is in that)

But {b,c,d} is rejected (it has 2 from the list a,b,c)

Example: no 3,a,b,c

Allows all of these:

{a,b,d} {a,b,e} {a,c,d} {a,c,e} {a,d,e} {b,c,d} {b,c,e} {b,d,e} {c,d,e}

Only {a,b,c} is missing because that is the only one that has 3 from the list a,b,c

The "pattern" Rule

The word "pattern" followed by a space and a list of items separated by commas.

You can include these "special" items:

• ? (question mark) means any item. It is like a "wildcard".
• * (an asterisk) means any number of items (0, 1, or more). Like a "super wildcard".

Example: pattern ?,c,*,f

Means "any item, followed by c, followed by zero or more items, then f"

So {a,c,d,f} is allowed

And {b,c,f,g} is also allowed (there are no items between c and f, which is OK)

But {c,d,e,f} is not, because there is no item before c.

Example: how many ways can Alex, Betty, Carol and John be lined up, with John after Alex.

Use: n=4, r=4, order=yes, replace=no.

The result is:

{Alex,Betty,Carol,John} {Alex,Betty,John,Carol} {Alex,Carol,Betty,John} {Alex,Carol,John,Betty} {Alex,John,Betty,Carol} {Alex,John,Carol,Betty} {Betty,Alex,Carol,John} {Betty,Alex,John,Carol} {Betty,Carol,Alex,John} {Carol,Alex,Betty,John} {Carol,Alex,John,Betty} {Carol,Betty,Alex,John}

Combination Calculator

What is a combination - combination definition, how to calculate combinations - combination formula, permutation and combination, permutation and combination with repetition. combination generator, combination probability and linear combination.

This combination calculator (n choose k calculator) is a tool that helps you not only determine the number of combinations in a set (often denoted as nCr), but it also shows you every single possible combination (or permutation) of your set, up to the length of 20 elements. However, be careful! It may take even a couple of seconds to find such long terms for our combination generator. If you wonder how many different combinations can be possibly made of a specific number of elements and sample size, try our combination calculator now!

If you're still not sure what a combination is, it will all be explained in the following article. You'll find here a combination definition together with the combination formula (with and without repetitions). We'll show you how to calculate combinations, and what the linear combination and combination probability are. Finally, we will talk about the relation between permutation and combination. Briefly, permutation takes into account the order of the members and combination does not . You can find more information below!

Have you ever wondered what your chances are of winning the main prize in a lottery? How probable is winning the second prize? To answer both and similar questions, you need to use combinations. We've got a special tool dedicated to that kind of problem. Our lottery calculator doesn't only estimate the combination probability of winning any lottery game but also provides a lottery formula. Try it! You'll find out how big (or small) those numbers are, in fact.

The combination definition says that it is the number of ways in which you can choose r elements out of a set containing n distinct objects (that's why such problems are often called "n choose r" problems). The order in which you choose the elements is not essential as opposed to the permutation (you can find an extensive explanation of that problem in the permutation and combination section).

Seeking for every combination of a set of objects is a purely mathematical problem. You probably have already been taught, say, how to find the greatest common factor (GCF) or how to find the least common multiple (LCM). Well, a combination is an entirely different story. Let's see how complicated it might be.

Imagine a bag filled with twelve balls, where each one is a different color. You pick five balls at random. How many distinct sets of balls can you get? Or, in other words, how many different combinations can you get?

Mathematicians provide the exact solution for many various problems, e.g., how to calculate square footage or how to calculate volume. Is there a similar approach to estimating the number of combinations in the above example with balls?

Luckily, you don't have to write down all of the possible sets! How to calculate the combinations, then? You can use the following combination formula that will allow you to determine the number of combinations in no time:

• C ( n , r ) C(n,r) C ( n , r ) is the number of combinations;
• n n n is the total number of elements in the set; and
• r r r is the number of elements you choose from this set.

The exclamation mark ! ! ! represents a factorial. Check out our factorial calculator for more information on this topic. The expression on the right-hand side is also known as the binomial coefficient .

Let's apply this equation to our problem with colorful balls. We need to determine how many different combinations there are:

You can check the result with our nCr calculator. It will list all possible combinations , too! However, be aware that 792 different combinations are already quite a lot to show. To avoid a situation where there are too many generated combinations, we limited this combination generator to a specific, maximum number of combinations (2000 by default). You can change it in the advanced mode whenever you want.

You may notice that, according to the combinations formula, the number of combinations for choosing only one element is simply n n n . On the other hand, if you have to select all the elements, there is only one way to do it. Let's check this combination property with our example. You've got the total number of objects that equals n = 12 n = 12 n = 12 . Every letter displayed in the nCr calculator represents a distinct color of a ball, e.g., A is red, B is yellow, C is green, and so on. If you choose only one element r = 1 r = 1 r = 1 at once from that set, the number of combinations will be 12 12 12 - because there are 12 different balls. However, if you choose r = 12 r = 12 r = 12 elements, there'll be only 1 1 1 possible combination that includes every ball. Try it by yourself with the n choose r calculator!

By this point, you probably know everything you should know about combinations and the combination formula. If you still don't have enough, in the next sections, we write more about the differences between permutation and combination (that are often erroneously considered the same thing ), combination probability, and linear combination.

Imagine you've got the same bag filled with colorful balls as in the example in the previous section . Again, you pick five balls at random, but this time, the order is important - it does matter whether you pick the red ball as first or third. Let's take a more straightforward example where you choose three balls called R(red), B(blue), G(green). There are six permutations of this set (the order of letters determines the order of the selected balls): RBG, RGB, BRG, BGR, GRB, GBR, and the combination definition says that there is only one combination! This is the crucial difference.

By definition, a permutation is the act of rearrangement of all the members of a set into some sequence or order. However, in literature, we often generalize this concept, and we resign from the requirement of using all the elements in a given set. That's what makes permutation and combination so similar. This meaning of permutation determines the number of ways in which you can choose and arrange r elements out of a set containing n distinct objects. This is called r-permutations of n (sometimes called variations). If you're after an even more in-depth explanation, the permutation calculator should satisfy this need.

The permutation formula is as below:

Doesn't this equation look familiar to the combination formula? In fact, if you know the number of combinations, you can easily calculate the number of permutations:

If you switch on the advanced mode of this combination calculator, you will be able to find the number of permutations.

You may wonder when you should use permutation instead of a combination . Well, it depends on whether you need to take order into account or not. For example, let's say that you have a deck of nine cards with digits from 1 to 9. You draw three random cards and line them up on the table, creating a three-digit number, e.g., 425 or 837. How many distinct numbers can you create?

Check the result with our nCr calculator! And how many different combinations are there?

The number of combinations is always smaller than the number of permutations. This time, it is six times smaller (if you multiply 84 by 3 ! = 6 3! = 6 3 ! = 6 , you'll get 504). It arises from the fact that every three cards you choose can be rearranged in six different ways, just like in the previous example with three color balls.

To complete our considerations about permutation and combination, we have to introduce a similar selection, but this time with allowed repetitions . It means that every time after you pick an element from the set of n distinct objects, you put it back to that set. In the example with the colorful balls, you take one ball from the bag, remember which one you drew, and put it back to the bag. Analogically, in the second example with cards, you select one card, write down the number on that card, and put it back to the deck. In that way, you can have, e.g., two red balls in your combination or 228 as your permutation.

You probably guess that both formulas will get much complicated. Still, it's not as sophisticated as calculating the alcohol content of your homebrew beer. In fact, in the case of permutation, the equation gets even more straightforward. The formula for combination with repetition is as follows:

and for permutation with repetition:

In the picture below, we present a summary of the differences between four types of selection of an object: combination, combination with repetition, permutation, and permutation with repetition . It's an example in which you have four balls of various colors, and you choose three of them. In the case of selections with repetition, you can pick one of the balls several times. If you want to try with the permutations, be careful, there'll be thousands of different sets! However, you can still safely calculate how many of them are there (permutations are in the advanced mode ).

Let's start with the combination probability, an essential in many statistical problems. An example pictured above should explain it easily - you pick three out of four colorful balls from the bag. Let's say you want to know the chances (probability) that there'll be a red ball among them. There are four different combinations, and the red ball is in the three of them. The combination probability is then:

If you draw three random balls from the bag, in 75% of cases, you'll pick a red ball. To express probability, we usually use the percent sign.

Now, let's suppose that you pick one ball, write down which color you got, and put it back in the bag. What's the combination probability that you'll get at least one red ball? This is a 'combination with repetition' problem. From the picture above, you can see that there are twenty combinations in total and red ball is in ten of them, so:

Is that a surprise for you? Well, it shouldn't be. When you return the first ball, e.g., blue ball, you can draw it as a second and third ball too. The chances of getting a red ball are thus lowered . You can do analogical considerations with permutation. Try to solve a problem with the bag of colorful balls: what is the probability that your first picked ball is red?

Let's say you don't trust us, and you want to test it yourself. You draw three balls out of four, and you check whether there is a red ball or not (like in the first example of this section). You repeat that process three more times, and you get the red ball only in one of four cases - 25 % 25\% 25% of cases. You expected 75 % 75\% 75% according to theory. What happened? Well, this is how probability works! There is the law of large numbers that describes the result of performing the same experiment a large number of times. If you repeat drawing, e.g., one hundred times, you'll be much closer to 75 % 75\% 75% .

What's more, the law of large numbers almost always leads to the standard normal distribution, which can describe, for example, intelligence or the height of people, with a so-called p-value . Keen to learn more? Normal distribution calculator is the place to go!

Have you ever heard about the linear combination? In fact, despite it have the word combination , it doesn't have much in common with what we have learned so far. Nevertheless, we'll try to explain it briefly. A linear combination is the result of taking a set of terms and multiplying each term by a constant and adding the results . It is frequently used in wave physics to predict diffraction grating equation or even in quantum physics because of the de Broglie equation. Here, you can see some common examples of linear combination:

• Vectors . Every vector in 3D can be decomposed into three unit vectors e ˆ 1 = ( 1 , 0 , 0 ) \^e_1 = (1,0,0) e ˆ 1 ​ = ( 1 , 0 , 0 ) , e ˆ 2 = ( 0 , 1 , 0 ) \^e_2 = (0,1,0) e ˆ 2 ​ = ( 0 , 1 , 0 ) and e ˆ 3 = ( 0 , 0 , 1 ) \^e_3 = (0,0,1) e ˆ 3 ​ = ( 0 , 0 , 1 ) . For example, v ⃗ = ( 2 , 5 , 3 ) = 2 e ˆ 1 + 5 e ˆ 2 + 3 e ˆ 3 \vec{v} = (2,5,3) = 2\^e_1 + 5\^e_2 + 3\^e_3 v = ( 2 , 5 , 3 ) = 2 e ˆ 1 ​ + 5 e ˆ 2 ​ + 3 e ˆ 3 ​ and that's linear combination.
• Functions . Let's say you've got two functions f ( x ) = e x f(x) = \text{e}^x f ( x ) = e x and g ( x ) = e − x g(x) = \text{e}^{-x} g ( x ) = e − x . From those two functions you can create linear combinations that describe the hyperbolic sine sinh ⁡ ( x ) = f ( x ) 2 − g ( x ) 2 \sinh(x) = \frac{f(x)}{2} - \frac{g(x)}{2} sinh ( x ) = 2 f ( x ) ​ − 2 g ( x ) ​ or cosine cosh ⁡ ( x ) = f ( x ) 2 + g ( x ) 2 \cosh(x) = \frac{f(x)}{2} + \frac{g(x)}{2} cosh ( x ) = 2 f ( x ) ​ + 2 g ( x ) ​ . You can do a similar thing with the normal sine and cosine, but you need to use the imaginary number i i i . We write about it more in the last section of the square root calculator .
• Polynomials . For example, you've got three polynomials p 1 ( x ) = 1 p_1(x) = 1 p 1 ​ ( x ) = 1 , p 2 ( x ) = 3 x + 3 p_2(x) = 3x + 3 p 2 ​ ( x ) = 3 x + 3 , p 3 ( x ) = x 2 − x + 1 p_3(x) = x^2 -x + 1 p 3 ​ ( x ) = x 2 − x + 1 and you want to express the function q ( x ) = 2 x 2 + x + 3 q(x) = 2x^2 + x + 3 q ( x ) = 2 x 2 + x + 3 as a linear combination of those polynomials. It's not always possible to do so, but in this case q ( x ) = − 2 p 1 ( x ) + p 2 ( x ) + 2 p 3 ( x ) q(x) = -2p_1(x) + p_2(x) + 2p_3(x) q ( x ) = − 2 p 1 ​ ( x ) + p 2 ​ ( x ) + 2 p 3 ​ ( x ) .

What is the difference between permutation and combination?

The fundamental difference between combinations and permutations in math is whether or not we care about the order of items :

• In permutation the order matters, so we arrange items in sequential order.
• In combinations the order does not matter, so we select a group of items from a larger collection.

How do I calculate permutations from combinations?

If you already have a combination and want to turn it into a permutation, you need to impose order on the set of items, i.e., choose one of the possible orderings for your set. Hence, the number of permutations of r items chosen from n items is equal to the number of combinations of r items chosen from n items multiplied by the number of orderings of these r items, i.e., by r! .

How do I calculate combinations from permutations?

If you already have a permutation and want to turn it into a combination, you need to remove order , i.e., regard all possible reorderings as the same object. Hence, the number of combinations of r items chosen from n items is equal to the number of permutations of r items chosen from n items divided by the number of orderings of these r items, i.e., by r! .

How many ways can I arrange a 7 letter word?

If the word has seven distinct letters, you have 7! = 5040 ways of arranging them (simple permutations of seven items). However, if some letters appear more than once, the number of arrangements gets reduced! For instance:

• If the word is "WITNESS", we have "S" appearing twice, so we divide 7! by 2! = 2 and the result is 2520 .
• If the word is "SOMEONE", we have "O" and "E" appearing twice, so we divide 7! by 2! ⋅ 2! = 4 and the result is 1260 .
• If the word is "UNKNOWN", we have "N" thrice, so we divide 7! by 3! = 6 and the result is 840 .

Car vs. Bike

Empirical rule, permutation with repetition.

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50 Fun Hands-On Activities and Games To Teach Multiplication

Making it fun makes it stick!

Multiplication is a basic skill students need to master before they can move on to more advanced math. Memorizing multiplication tables is one option, but it’s important for kids to understand exactly what it means to multiply. This list of fun and engaging ways to teach multiplication has so many options. You’re sure to find a way to resonate with every one of your students!

1. Play a game of Scoot

This is a fun way to break up the routine of worksheets. One at a time, you will post one of the multiplication task cards and your students will work to find the answer. After a set amount of time (up to you), say “Scoot.” Students will leave their answer sheet on their desk and move one seat to their left. Post another task card. Again, say “Scoot” and have students rotate.

2. Practice skip-counting with a song

For many of us, setting information to music helps us memorize it. This series of videos from HeavenSentHorse features common tunes that your students will quickly catch on to like Jingle Bells, This Old Man and more.

3. Solve multiplication puzzles

Puzzles are a great way to engage students and build their problem-solving skills. These puzzles help students put together the pieces to get the whole picture and really understand how to solve a multiplication problem.

4. Play Four in a Row

This fun game challenges kids to practice their math facts. Partners will take turns choosing a circle and solving the math fact. If they get it right, they place a marker over it (here, a penguin stamp). The first player to connect four wins.

5. Solve Mystery Pictures

Students will solve the one-digit multiplication problems, then use the key to color in the boxes and create the mystery picture.

6. Play multiplication tic-tac-toe

Playing with partners, each player chooses a multiplication problem to solve. If they get it right, they mark it with their dot marker. If not, it’s the next person’s turn. Play goes back and forth until someone gets three in a row.

7. Build multiplication skills with Minecraft

Your kids will flip for this fun version of Minecraft multiplication. Download the game and instructions for free!

8. Deal a hand of Spiral

Players take turns rolling the dice and moving around the game board with this fun multiplication card game.

9. Sweeten up multiplication practice

Write multiplication problems on the bottom of small cupcake paper liners. On the inside, write the product. Two players take turns picking a liner, finding the answer, and flipping it over to check.

10. Take a whirl at fidget spinner math

The object of the game is simple: Spin the spinner and complete as many problems as possible.

11. Make multiplication pool noodles

Pick up some pool noodles and use our easy tutorial to turn them into the ultimate multiplication manipulatives ! This is such a unique way for kids to practice their math facts.

12. Match wits at Array Capture

You can use dice-in-dice or just a regular pair of dice for this game. Players roll the dice and use the numbers to block off space on the grid, writing in the math sentence too. At the end of the game, the player with the most spaces colored in wins.

13. Punch holes to make arrays

Arrays introduce multiplication in a way that kids can easily understand. This activity is great for active learners who will love punching holes as they create multiplication arrays for basic facts.

14. Fold a multiplication cootie catcher

We love finding new and clever ways to practice math facts! Get these free printables , then let kids color and fold them up. Now they’ve got self-checking practice at their fingertips.

15. Visit the Multiplication Shop

How fun is this? Set up a “store” with small items for sale. Kids choose a number of items from each section to “buy” and write out the multiplication sentences as their receipt!

16. Ask a partner, “Do You Have …?”

Got an old “Guess Who?” game lying around? Turn it into a multiplication game instead!

17. Pull out the base-10 blocks

Base-10 blocks are one of our favorite manipulatives, and they’re a terrific tool to help you teach multiplication. Build arrays with them to let kids visualize the problems and their answers.

18. Color in Emoji Mystery pages

Here’s a twist on color-by-number. First, kids have to answer the multiplication problems in each square. Then they get to color! Get a free set of these pages at Artsy Fartsy Mama .

19. Multiply with dice-in-dice

Something about dice-in-dice just makes learning more fun! If you don’t have a set, you can use a pair of regular dice for this activity. Mix things up with polyhedral dice with higher numbers too.

20. Pick sticks to play Kaboom!

So easy and so fun! Write multiplication facts at the end of a variety of wood craft sticks. On a few, write “Kaboom!” instead. To play, kids draw sticks from a cup and answer the problem. If they get it right, they can keep pulling sticks. But if they get a Kaboom! stick, they have to put their whole collection back!

21. Match Multiplication memory cards

Practice facts with a memory game. Make your own cards by writing facts and answers, then lay them all face down. Turn over a card and try to find its matching answer or problem. Your turn continues as long as you’re able to make matches.

22. Find it first

Write a series of products on the whiteboard, and mix in a few random numbers too. Send two students up to the board and call out a multiplication problem. The first one to find and point to the correct answer wins a point.

23. Draw Waldorf multiplication flowers

This is a creative way to teach multiplication facts. Draw a flower with 12 petals and a circle in the center. In the circle, write the multiplicand; on the petals, the numbers 1 to 12. Now, draw larger petals outside, and fill in the product of each fact. Add some color to make fun classroom decorations!

24. Play multiplication war

All you need for this is a deck of cards, plus paper and a pencil for each player. Split the deck between the players. Each player flips two cards, then writes out the multiplication sentence and the answer. The player with the higher product takes all the cards. Play until the deck is gone. The player with the most cards wins!

25. Compete at multiplication bingo

Grab these free printable bingo cards at the link and provide one to each student along with some chips or beans to use as counters. Call out multiplication facts and have students cover the answers if they have them. When they get five in a row, it’s a bingo!

26. Put a twist on Rock, Paper, Scissors

Chances are your students already know how to play Rock, Paper, Scissors. This is similar, but instead, each player holds out a random number of fingers. The first one to correctly multiply them together and call out the answer wins a point. Play to 5, 10, or any number you choose.

27. Do some egg carton multiplication

Number the cups of an egg carton from 1 to 12. Drop in two marbles or beans, then close the carton and shake it up. Open it up and have students write out the multiplication number sentence based on where the marbles landed. This is an easy tool parents can make for kids at home too.

28. Try interactive flash cards

These aren’t your ordinary flash cards! These free printables are a cool way to teach multiplication since the answer side includes a dot array to help kids visualize the solution. You can use sticky-note flags to cover the answers while kids use the arrays for help too.

29. Teach multiplication facts with a paper plate wheel

All it takes is paper plates, glue, and a marker to help your students learn their multiplication tables. Let kids have fun decorating their plates, and this doubles as a math craft!

30. Practice with fact family triangles

Tie together multiplication and division facts with triangle flash cards. Learn how to use them and buy a printable set at Primary Flourish . You can also have kids make their own.

31. Make LEGO arrays

LEGO bricks are one of our favorite ways to teach math! You can use multiple bricks to make arrays or just look at the bumps on the top of a single brick as an array in itself.

32. Try the finger trick

This cute craft also teaches kids a clever multiplication trick that can help them if they’re stuck with multiplication “times nine.” Learn the easy trick at 5-Minute Crafts .

33. Use the Force to teach multiplication

Sometimes learning multiplication facts just takes practice. Worksheets may not be very exciting, but adding a theme that kids are interested in may motivate your students. This free download from Royal Baloo features homework sheets and practice papers with graphs, mazes, puzzles, and more, all with a Star Wars theme.

34. Watch a multiplication video

From Schoolhouse Rock to Animaniacs and beyond, there are lots of fun videos to help you teach multiplication. Find our big list here.

35. Play multiplication checkers

Turn a thrift store checkerboard into a multiplication game with some stickers and a marker. The play is similar to traditional checkers, but you have to solve the problem before you can leave your checker on a new space.

36. Toss a multiplication soccer ball

What better way to appeal to students than to combine math with one of their favorite activities? These fun balls can be used in so many ways to support learning.

37. Flip bottle caps

Here’s a cool alternative to flash cards. You can use metal bottle caps or plastic bottle lids, along with round stickers that fit the caps. It’s a great way to go green while you teach multiplication!

38. Batter up to learn multiplication

Sports-loving kids will love this one! Get the free printables and use them along with a 10-sided die to get some multiplication facts practice.

39. Line up dominoes

Single dominoes turned sideways become multiplication number sentences! Grab a handful and have kids write out the sentences and their answers.

40. Roll to win

This works a bit like Yahtzee. Roll a die, then choose a number from 1 to 6 to multiply it by. Each number can only be used once, so choose carefully to rack up the most points. If you have polyhedral dice, you can play with higher numbers too.

41. Sculpt play dough arrays

What kid doesn’t love the chance to play with play dough? Use this activity for math centers, and kids will really enjoy practicing their multiplication facts.

42. Connect the dots with Multiplication Squares

This is a math spin on the old Dots and Boxes game. Kids roll two dice and multiply the numbers together. Then they find the answer on the board and connect two dots next to it. The goal is to complete a box, coloring it in with your own color marker. When the board is full, count the squares to see who wins.

43. Cut out and assemble array cities

Here’s another colorful math craft: multiplication array cities. Most high-rises have their windows arranged to make perfect arrays. Have kids make their own city skylines with buildings showing various multiplication arrays.

44. Stack math power towers

There’s a universal appeal about making stacks of cups, so don’t be surprised if kids clamor to play this game over and over again. Pull a cup, answer correctly, and stack. See who can get a stack of 10 first, or who can build the highest tower in 2 minutes, and so on.

45. Change your students’ names (temporarily)

Grab some name tags and write multiplication equations on each. Give a tag to each of your students. For the remainder of the day, everyone will refer to each other by the answer to the equation on their tag (e.g., the student with the name tag that says 7 x 6 would be referred to as “42”).

46. Take multiplication to the gridiron

All you need is poster board, 12-sided dice, and a couple of game pieces to teach multiplication using football. Students move their game piece up the field by rolling the dice and multiplying the two numbers that face up. They get four chances to score a touchdown.

47. Roll and Bump!

Print the free game boards , each with a multiplier in the heading. Roll two dice, add them together, then multiply by the multiplier. Then place your game piece over that answer. If another player also comes up with the same product, they can “bump” your game piece off and replace it with their own. The player with the most markers on the board at the end of the game wins.

48. Weave multiplication patterns

Skip-counting provides an introduction to multiplication. We love this hands-on activity where kids skip-count and weave yarn into pretty patterns.

49. Challenge kids with Multiplication Jenga

Grab an old Jenga game at the thrift store (or pick up the generic version at the dollar store). Write multiplication problems on each block, then stack ’em up. Player one pulls a block and tries to answer the problem. If they get it right, they keep the block. If they miss, their partner gets a chance. But if no one can answer it, the block gets stacked up on top. Keep playing until the tower collapses!

50. Twist and learn

Your students will love this twisted version of an old favorite! The original Math Twister was designed for addition, but it works for multiplication too. Simply write products on sticky notes and add them to circles. Then call out math problems like “Left foot, 4 x 5!” The player must put their left foot on the number 20—if they can!

Looking for more activities to teach multiplication? Try these Teacher-Tested Tips and Activities for Teaching the Area Model Multiplication Method .

Plus, get all the latest teaching tips and ideas when you sign up for our free newsletters .

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How to prioritize savings for different life goals

36% of americans are prioritizing their emergency savings account and debt repayment this year.

(InvestigateTV) — When creating a financial plan, many experts suggest setting up short-term and long-term financial goals.

Building up a $500 emergency fund is the prime example of a short-term goal. Other objectives include paying down credit card debt, or saving for travel or a wedding.

Michael Joyce with the financial firm Agili said all those goals have a clear end date.

He thinks of these goals as “sleep at night” money.

“Pretty safe and you know it’s there when you need it,” Joyce commented. “So, if you know you’re going on a big vacation a year from now and you’re saving it for that. You should put that in more or less ‘sleep at night’ money.”

Joyce said saving for long-term goals typically means you are saving for your retirement fund, paying off a mortgage, starting a business or even saving for children’s college tuition.

“If the other funds were your ‘sleep at night’ money, these are your ‘eat better in ten years’ money’” Joyce quipped. “Where you’re going to be taking a little bit of risk with the hope that you’re going to get higher returns.”

Joyce said saving for these types of long-term goals usually means investing money to see it grow in a much different way than it would in a savings account.

For short-term goals and emergency funds, keep money somewhere it can be quickly accessed without penalty, like a savings account.

Copyright 2024 Gray Media Group, Inc. All rights reserved.

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Money blog: 600 new skyscrapers 'on way' for London, report finds

A reader seeks help as her employer of 24 years is bringing in a new clock-in system to pay her by the minute. Read this and all the latest personal finance and consumer news in the Money blog - and share your own problem or dispute below.

Monday 13 May 2024 19:57, UK

• Gen Z would rather deliver parcels than work in restaurants, Michel Roux Jr claims
• 600 new skyscrapers on way for London, report finds
• Money Problem: My workplace is bringing in new clock-in system to pay us by the minute - is this allowed?
• Free childcare applications open for new age band

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• Best of the Money blog - an archive

Ask a question or make a comment

Young homebuyers are being forced to gamble with their retirement prospects by taking on ultra-long mortgages, according to a former pensions minister.

Sir Steve Webb described data - supplied by the Financial Conduct Authority to the Bank of England - as "shocking".

It suggests that more than one million new mortgages have been issued over the past three years with end dates beyond the state pension age.

The ex-Liberal Democrat MP, who is now a partner at the consultancy firm LCP, voiced fears that borrowers could be forced to raid their pension savings to clear their mortgage in a worst-case scenario.

Sir Steve saw the potential for harm in any case, as longer-term mortgages deprive people of a period running up to retirement when they could be mortgage-free and boosting their pension.

What does the data say? 

• 42% of new mortgages in the fourth quarter of 2023 - or 91,394 - had terms going beyond the state pension age;
• In the final quarter of last year, people aged 30 to 39 accounted for 30,943 new mortgages lasting beyond state pension age;
• People aged 40 to 49 accounted for 32,305;
• Under-30s made up 3,676 of these mortgages;
• People aged 50 to 59 accounted for 18,854, and there were 661 who were over 70.

Mortgage rates have been rising since the end of 2021 when the Bank of England began action to tackle rising inflation.

Taking home loans with longer maturity dates tends to be more attractive when interest rates are high, as monthly repayments are lower.

You can read more on this story below...

Waitrose has become the only supermarket to receive a royal warrant from the King. 

The recognition means the company has regularly provided the royal household with products for at least five years. 

It also means it can use the King's coat of arms on packaging, as part of advertising or on any stationary it creates. 

Waitrose was first granted a royal warrant in 1928 for supplying King George V with groceries and cleaning materials.

"We are honoured and proud that His Majesty has granted us his warrant," James Bailey, executive director of Waitrose, said. 

"It means the world to all of us, and our farmers and suppliers. There couldn’t be a more powerful symbol of our commitment to service and quality, and our determination to have the highest environmental and animal welfare standards." 

Waitrose was previously granted a royal warrant by the late Queen in 2002 and the King when he was Prince of Wales in 2010.

The Queen has also granted her first royal warrants, picking seven companies, including luxury department store Fortnum & Mason and the florist that supplied her coronation flowers, Shane Connolly & Company. 

The royal nod could be bad news for customers, however, with a brand finance expert telling Sky News that having a royal warrant allows firms to charge a price premium.

David Haigh said his company's research estimated this to be "between 10% and 25%".

A royal warrant says a company or a product is luxurious, high quality and sustainable, he explained. 

He estimates the scheme is "worth billions to UK companies and… therefore it's a very high value to the UK economy".

"And one of the reasons for that is that a lot of foreign tourists and buyers have a preference for royal warrant holder products. We found that 100% of Chinese buyers would pay in excess of 10% for a royal warrant holder product."

Read more on the Queen's choices here :

Gordon Ramsay's restaurants tripled losses to £3.4m last year, as the chef warned businesses in the industry were facing a "challenging" climate. 

The chef's group spent millions opening five new restaurants in 2023, including a Lucky Cat in Manchester, a Bread Street Kitchen in Battersea Power Station and a Street Pizza in Edinburgh. 

Sales at his wide-ranging establishments rose, however, by 21% to £95.6m in the year to August, according to The Telegraph. 

"It's been a really hard-fought year, but at the same time an exciting year, and in tough times it amazes me how strong and vibrant our industry is," Ramsay told the news outlet. 

"It's challenging out there and businesses are battling to stay afloat, rising costs, rent and food costs, multiple strikes. It's a battle" 

He was optimistic, however, saying there hasn't been "so much passion and vibrancy" in the industry since he opened his first restaurant in 1998.

"We've still got something wonderful to celebrate, and I truly believe the industry has never been so exciting."

Once the UK's favourite alcoholic beverage, beer's popularity seems to be fading among the younger drinking generation... 

In fact, only 30% of people aged 18 to 24 ever drink it, according to a study commissioned by the Society of Independent Brewers. 

Instead, younger drinkers say they prefer drinking spirits, wine and cider. 

Pub visits appear to be suffering as well, with almost a quarter of the 2,000 people surveyed saying they have never visited their local. 

SIBA's 2024 Craft Beer Report paints a more positive picture for small and independent brewers, however, with more than 55% of beer consumers saying they now drink "local craft beer". 

It also found average beer production volumes among independent breweries has risen by 14% since last year - a return to pre-pandemic levels for the first time in 4 years. 

"Demand for local, independently brewed beer in the UK is strong, with independent brewers reporting production volumes up by 14%, meaning they have returned to 2019 volumes again," Andy Slee, SIBA's chief executive, said. 

But, he said, it's time for "cautious optimism" only, with the industry still plagued with a number of issues. 

"The short-term issue for small independent breweries isn't demand; it's profitability, rising costs and financial pressures such as lingering COVID debt," he said. 

"Far too many breweries are simply trying to survive rather than thrive, so while there are many positives signs highlighted in the report, for now it's cautious optimism."

Earlier this year, our Money reporter Emily Mee explored whether the UK's big night out culture was dying out. 

Nightlife experts warned we're losing one club every two days at the moment - and if we stay on this trajectory, we will have none left by 2030.

You can read more about her findings here...

A total of 583 skyscrapers are "queuing up in the pipeline" to be built across central London, a development thinktank has said. 

That is more than double the 270 built in the past decade. 

In the eastern borough of Tower Hamlets alone, 71 tall buildings were completed in that time that time, the report by New London Architecture found. 

A further 24 were in the City of London and 27 in Canary Wharf and Isle of Dogs. 

The report said the rapid change has been fuelled by a "burgeoning demand" for office and residential space, overseas investment and a supporting planning environment. 

"Tall buildings have changed the face of London substantially over the last 20 years and will continue to do so - the pipeline that NLA has tracked means there is at least 10 years' supply that has already been defined," Peter Murray, the organisation's co-founder, said. 

"London's population continues to grow, passing the 10 million mark at the end of this decade.

"We'll still need tall buildings; and NLA will continue to keep a close watch on what's going on." 

Restaurants might only be able to open three or four days a week due to staffing problems, Michel Roux Jr has warned. 

Speaking to The Telegraph as he gears up to open his new restaurant Chez Rouz, the Michelin starred chef admitted the industry needs to change to accommodate flexible working hours. 

"Just because I worked 80 hours a week or more doesn't mean the next generation should," he said. 

"Quite the contrary. That is something that we have to address in our industry."

But, he warned that the move will come at a cost... 

"It will mean ultimately that going out is going to be more expensive, and that maybe your favourite restaurant is no longer open seven days a week - it's only open three or four days a week," he said. 

The industry is known for its long, unsociable working hours, and Roux Jr explained that the real issue hit after the pandemic, with people no longer wanting to work weekends. 

"People don't want to work unsociable hours and would rather work delivering parcels as and when they want to. It's as simple as that," he added. 

Earlier this year, Roux Jr said goodbye to his famous restaurant Le Gavroche in London. 

It had been opened by his father Albert Roux and uncle Michel Roux in 1967. 

Now, he said it's "brave" to open a new restaurant, with the market "very, very tough". 

"I really feel for anyone that is brave enough to open up a restaurant now. It's incredibly difficult," he added. 

Chez Rouz at The Langham in Marylebone, central London, is due to open on 22 May. 

By James Sillars , business news reporter

A pause for breath on the FTSE 100 after a 3% gain over the course of past week that took the index to a fresh record closing high.

The rally of recent weeks - significant for London's standing and pension pots alike - has been broad based and reflects several factors.

A major driver has been sterling's weakness versus the US dollar.

The US currency has been strong as the Federal Reserve, its central bank, has hinted it will be some time yet before it begins to cut interest rates.

Language out of the Bank of England last week sparked a flurry of bets that UK rates could be cut as early as next month.

A weaker pound boosts dollar-earning constituents on the FTSE 100 because they get more for their money when dollars are converted to pounds.

Also at play is the view that UK stocks represent good value, as they are cheaper compared to many of their international peers.

A few moments ago, the FTSE 100 was trading 6 points lower at 8,423.

A major talking point is the possibility of the Chinese fast fashion firm Shein listing in London.

According to Reuters, the company has shifted its focus to the UK after receiving a lukewarm reception in the United States.

The news agency, citing two sources, reported that Shein was stepping up its preparations for an initial public offering in London that would be expected to be one of the biggest carried out globally this year.

By Emily Mee , Money team

No one likes the date in their calendar when their MOT rolls around. 

But to make things a little less stressful, consumer expert Scott Dixon - known as The Complaints Resolver - has given us some tips on what to look out for to help your vehicle pass with flying colours. 

Some of the most common failures are faulty steering, brakes, suspension, worn or damaged tyres, cracked windscreens and faulty lights. 

Mr Dixon recommends you get your car serviced a couple of weeks before your MOT, in case there are any complex or costly issues. 

This will give you time to get them fixed and get your car through first time without any advisories. 

Aside from taking your car for a service, there are also some easy checks you can run yourself... 

Listen for unusual clunks while you're driving - this could be a sign of a damaged suspension. 

You could also check by pushing the car down on each corner. It should return to normal without bouncing a few times. 

Another option is to look with a torch under the wheel arch, as this should reveal any obvious defects. 

Blown bulbs are a common MOT failure, but they're cheap to fix. 

Walk around your car and check all the bulbs are working - this includes the headlights, sidelights, brake lights, indicators and the number plate bulb.

Mr Dixon says it's "not an easy job" to change the lightbulbs yourself on most modern cars, as the MOT will also check the positioning of the light. Therefore he recommends getting this done professionally. 

Squealing or grinding noises may be a sign your brake pads need replacing. 

You should also check whether your car stops in a straight line, or whether it pulls in different directions. 

Don't forget about the handbrake, too. Test it out on a slope and see if it securely holds the car. If it doesn't, you should get it adjusted. 

It's easy to check if your wipers work okay, but you should also make sure to inspect the blades for tears and rips. 

They should be able to clean the windows with no smears. 

Mr Dixon says you don't need to pay Halfords to change your wiper blade as you can "do it yourself in seconds". All you need to do is look for a YouTube tutorial. 

He also recommends buying the Bosch wiper blades, as he says these are good quality and will also be a sign you've looked after your car well when you come to sell it. 

One thing to look out for is tread depth. You can do this by looking for the "wear bar" that sits between the tread. 

If it's close to 1.6mm and is low, you should get the tyre replaced so it's not flagged as an advisory. 

Also check for perished tyre walls, which can happen when a vehicle is standing for any length of time. 

Uneven tyre wear is another potential issue, and if there are signs of this you should get the tyre replaced and tracking and suspension checked. 

These must be in good condition and working order, with no tears or knots. 

Registration plates

Your number plates should be clean and visible with a working light bulb at the rear. You may need to give them a wipe and replace the bulb if necessary. 

This should be in good condition, without damage such as loose bumpers or sharp edges. 

Mr Dixon advises against using automatic car washes during your car's lifetime, saying they "wreck your car". 

"It's not just your paintwork but they can also damage the wiper blades and the bodywork," he says. 

Check for warning lights

You'll need to take your vehicle to a trusted garage or mechanic for this. 

Exhaust emissions

Some diesel vehicles can fail their MOTs based on emissions. To avoid this, you can buy a fuel treatment pack and take your car for a good run to clear the fuel lines and tank.

Driving for at least 30 to 50 minutes at a sustained speed on a motorway or A-road should help to clear the filter. 

You should make sure the driver's view of the road isn't obstructed, so check for stone chips at eye level and remove any obstructions such as air fresheners and mobile phone cradles. 

What else should you think about? 

Make sure your car is clean beforehand, as a tester can refuse to do your MOT if the vehicle is filthy and full of rubbish. 

Giving your car a clean can also give you a chance to inspect it, Mr Dixon says. 

Another thing to do is to check last year's MOT for any advisories that might crop up this time. 

These potential issues will still be there - so it's best not to ignore them. 

You can check your vehicle's MOT history using  https://car-check.co.uk . 

Every Monday we get an expert to answer your money problems or consumer disputes. Find out how to submit yours at the bottom of this post. Today's question is...

I have worked at a bank for 24 years - the facilities are outsourced. This new company is bringing in a system where the staff have to click in and out and are then paid by the minute? Is this allowed? Amber

Ian Jones, director and principal solicitor at Spencer Shaw Solicitors, has picked this one up...

Your rights depend on your contract and what it says about payment. Does it specify an annual salary, or payment by time? Does it allow for changes to how payment is calculated?

If the contract does not allow for this type of payment, your employer may be trying to vary the contract of employment unlawfully.

If you're directly employed by the bank, and your pay arrangements are changing because of a new monitoring system, this would be an internal contract variation. If you work in the facilities department and the new contractor is taking over as your employer, the Transfer of Undertakings (Protection of Employment) Regulations (TUPE) 2006 may apply. 

In this case, your current terms, conditions and previous service will transfer to the new employer.

TUPE may make the issue sound more complicated but, in practice, either way the changes will be valid only if the employee agrees to them.

If you have not agreed to the change, then this could be a breach of contract. This could give rise to a successful claim in the civil courts or the employment tribunal. 

If the breach is serious (for example, you're paid less than agreed in the original contract) and you resign in response, this could amount to constructive dismissal for which a claim can be made in the employment tribunal. 

It would be sensible to get the contract reviewed by a solicitor for advice. But act swiftly - if you continue working for the employer, you are effectively waiving the breach and accepting the change to your contract.

To make it possible to pay by the minute, employees may be monitored while at work. When collecting and processing data and using it to make a decision, the employer must comply with data protection laws. If not, the employee could be entitled to compensation, depending on the breach, or the employer could be at risk of a sanction by the regulator the Information Commissioner's Office.

This feature is not intended as financial advice - the aim is to give an overview of the things you should think about.  Submit your dilemma or consumer dispute via:

• The form above - make sure you leave a phone number or email address
• Email [email protected] with the subject line "Money blog"
• WhatsApp us  here .

Please make sure you leave your contact details as we cannot follow up consumer disputes without them.

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Solar Storm Intensifies, Filling Skies With Northern Lights

Officials warned of potential blackouts or interference with navigation and communication systems this weekend, as well as auroras as far south as Southern California or Texas.

By Katrina Miller and Judson Jones

Katrina Miller reports on space and astronomy and Judson Jones is a meteorologist.

A dramatic blast from the sun set off the highest-level geomagnetic storm in Earth’s atmosphere on Friday that is expected to make the northern lights visible as far south as Florida and Southern California and could interfere with power grids, communications and navigations system.

It is the strongest such storm to reach Earth since Halloween of 2003. That one was strong enough to create power outages in Sweden and damage transformers in South Africa.

The effects could continue through the weekend as a steady stream of emissions from the sun continues to bombard the planet’s magnetic field.

The solar activity is so powerful that the National Oceanic and Atmospheric Administration, which monitors space weather, issued an unusual storm watch for the first time in 19 years, which was then upgraded to a warning. The agency began observing outbursts on the sun’s surface on Wednesday, with at least five heading in the direction of Earth.

“What we’re expecting over the next couple of days should be more significant than what we’ve seen certainly so far,” Mike Bettwy, the operations chief at NOAA’s Space Weather Prediction Center, said at a news conference on Friday morning.

For people in many places, the most visible part of the storm will be the northern lights, known also as auroras. But authorities and companies will also be on the lookout for the event’s effects on infrastructure, like global positioning systems, radio communications and even electrical power.

While the northern lights are most often seen in higher latitudes closer to the North Pole, people in many more parts of the world are already getting a show this weekend that could last through the early part of next week.

As Friday turned to Saturday in Europe, people across the continent described skies hued in a mottling of colors.

Alfredo Carpineti , an astrophysicist, journalist and author in North London, saw them with his husband from the rooftop of their apartment building.

“It is incredible to be able to see the aurora directly from one’s own backyard,” he said. “I was hoping to maybe catch a glimpse of green on the horizon, but it was all across the sky in both green and purple.”

Here’s what you need to know about this weekend’s solar event.

How will the storm affect people on Earth?

A geomagnetic storm watch or warning indicates that space weather may affect critical infrastructure on or orbiting near Earth. It may introduce additional current into systems, which could damage pipelines, railroad tracks and power lines.

According to Joe Llama, an astronomer at Lowell Observatory, communications that rely on high frequency radio waves, such as ham radio and commercial aviation , are most likely to suffer. That means it is unlikely that your cellphone or car radio, which depend on much higher frequency radio waves, will conk out.

Still, it is possible for blackouts to occur. As with any power outage, you can prepare by keeping your devices charged and having access to backup batteries, generators and radio.

The most notable solar storm recorded in history occurred in 1859. Known as the Carrington Event, it lasted for nearly a week, creating aurora that stretched down to Hawaii and Central America and impacting hundreds of thousands of miles of telegraph lines.

But that was technology of the 19th century, used before scientists fully understood how solar activity disrupted Earth’s atmosphere and communication systems.

“That was an extreme level event,” said Shawn Dahl, a forecaster at NOAA’s Space Weather Prediction Center. “We are not anticipating that.”

Unlike tornado watches and warnings, the target audience for NOAA’s announcements is not the public.

“For most people here on planet Earth, they won’t have to do anything,” said Rob Steenburgh, a space scientist at NOAA’s Space Weather Prediction Center.

The goal of the announcements is to give agencies and companies that operate this infrastructure time to put protection measures in place to mitigate any effects.

“If everything is working like it should, the grid will be stable and they’ll be able to go about their daily lives,” Mr. Steenburgh said.

Will I be able to see the northern lights?

It is possible that the northern lights may grace the skies this week over places that don’t usually see them. The best visibility is outside the bright lights of cities.

Clouds or stormy weather could pose a problem in some places. But if the skies are clear, even well south of where the aurora is forecast to take place, snap a picture or record a video with your cellphone. The sensor on the camera is more sensitive to the wavelengths produced by the aurora and may produce an image you can’t see with the naked eye.

Another opportunity could be viewing sunspots during the daytime, if your skies are clear. As always, do not look directly at the sun without protection. But if you still have your eclipse glasses lying around from the April 8 event, you may try to use them to try to spot the cluster of sunspots causing the activity.

How strong is the current geomagnetic storm?

Giant explosions on the surface of the sun, known as coronal mass ejections, send streams of energetic particles into space. But the sun is large, and such outbursts may not cross our planet as it travels around the star. But when these particles create a disturbance in Earth’s magnetic field, it is known as a geomagnetic storm.

NOAA classifies these storms on a “G” scale of 1 to 5, with G1 being minor and G5 being extreme. The most extreme storms can cause widespread blackouts and damage to infrastructure on Earth. Satellites may also have trouble orienting themselves or sending or receiving information during these events.

The current storm is classified as G5, or “extreme.” It is caused by a cluster of sunspots — dark, cool regions on the solar surface — that is about 16 times the diameter of Earth. The cluster is flaring and ejecting material every six to 12 hours.

“We anticipate that we’re going to get one shock after another through the weekend,” said Brent Gordon, chief of the space weather services branch at NOAA’s Space Weather Prediction Center.

Why is this happening now?

The sun’s activity ebbs and flows on an 11-year cycle, and right now, it is approaching a solar maximum. Three other severe geomagnetic storms have been observed so far in the current activity cycle, which began in December 2019, but none were predicted to cause effects strong enough on Earth to warrant a watch or warning announcement.

The cluster of sunspots generating the current storm is the largest seen in this solar cycle, NOAA officials said. They added that the activity in this cycle has outperformed initial predictions .

More flares and expulsions from this cluster are expected, but because of the sun’s rotation the cluster will be oriented in a position less likely to affect Earth. In the coming weeks, the sunspots may appear again on the left side of the sun, but it is difficult for scientists to predict whether this will cause another bout of activity.

“Usually, these don’t come around packing as much of a punch as they did originally,” Mr. Dahl said. “But time will tell on that.”

Jonathan O’Callaghan contributed reporting from London.

An earlier version of this article misstated the radio frequencies used by cellphones and car radios. They are higher frequencies, not low.

How we handle corrections

Katrina Miller is a science reporting fellow for The Times. She recently earned her Ph.D. in particle physics from the University of Chicago. More about Katrina Miller

Judson Jones is a meteorologist and reporter for The Times who forecasts and covers extreme weather. More about Judson Jones

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